The Lognormal Diffusion Is Hardly an Equilibrium Price Process for Exhaustible Resources

In a model of a competitive spot market for an exhaustible resource under demand uncertainty, it is shown that the lognormal diffusion (the geometrical Brownian motion) can hardly be an equilibrium price process under the reasonable assumptions that suppliers choose the time to extract, and deposits have different costs. Each supplier will start extraction when price first exceeds a boundary, which depends on that supplier′s costs. But no new extraction will start during periods when the price is lower than the previously recorded high. It is highly unlikely that aggregate demand responds to prices in the same way as supply.